| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
In this research project, we investigated differential equations and difference equations associated with accessory parameters. An important example of the differential equations having an accessory parameter is Heun's differential equation. The q-Heun equation is a q-difference analogue of Heun's differential equation.
We obtained several results on the q-Heun equation and its variants from the perspective of the symmetry and the q-Painleve equations. We introduced the variants of the q-hypergeometric equation, and we investigated their solutions. The results between the q-middle convolution and the q-Heun equation were beyond our expectations.
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